Gravitational waves and the geometry of spacetime (2024)

Gravitational waves and the geometry of spacetime (1)

When speaking of our universe, it's often said that "matter tells spacetime how to curve, and curved spacetime tells matter how to move." This is the essence of Albert Einstein's famous general theory of relativity, and describes how planets, stars, and galaxies move and influence the space around them. While general relativity captures much of the big in our universe, it's at odds with the small in physics as described by quantum mechanics.

For his Ph.D. research, Sjors Heefer has explored gravity in our universe, with his research having implications for the exciting field of gravitational waves, and perhaps influencing how the big and small of physics can be reconciled in the future.

A little over a hundred years ago, Albert Einstein revolutionized our understanding of gravity with his general theory of relativity.

"According to Einstein's theory, gravity is not a force but emerges due to the geometry of the four-dimensional spacetime continuum, or spacetime for short," says Heefer. "And it's central to the emergence of fascinating phenomena in our universe such as gravitational waves."

Massive objects, such as the sun or galaxies, warp spacetime around them, and other objects then move along the straightest possible paths—otherwise known as geodesics—through this curved spacetime.

Due to the curvature, however, these geodesics are not straight in the usual sense at all. In the case of the planets in the solar system, for instance, they describe elliptical orbits around the sun. In this way, general relativity elegantly explains the movement of the planets as well as numerous other gravitational phenomena, ranging from everyday situations to black holes and the Big Bang. As such, it remains a cornerstone of modern physics.

Clash of the theories

While general relativity describes a host of astrophysical phenomena, it clashes with another fundamental theory of physics—quantum mechanics.

"Quantum mechanics suggests that particles (like electrons or muons) exist in multiple states at the same time until they are measured or observed," says Heefer. "Once measured, they randomly select a state due to a mysterious effect referred to as the 'collapse of the wave function.'"

In quantum mechanics, a wave function is a mathematical expression that describes the position and state of a particle, such as an electron. And the square of the wave function leads to a collection of probabilities of where the particle might be located. The larger the square of the wave function at a particular location, the higher the probability that a particle will be located at that location once it is observed.

"All matter in our universe appears to be subject to the strange probabilistic laws of quantum mechanics," Heefer notes. "And the same is true for all forces of nature—except for gravity. This discrepancy leads to deep philosophical and mathematical paradoxes, and resolving these is one of the primary challenges in fundamental physics today."

Is expansion the solution?

One approach to resolving the clash of general relativity and quantum mechanics is to expand the mathematical framework behind general relativity.

In terms of mathematics, general relativity is based on pseudo-Riemannian geometry, which is a mathematical language capable of describing most of the typical shapes that spacetime can take.

"Recent discoveries indicate, however, that our universe's spacetime might be outside the scope of pseudo-Riemannian geometry and can only be described by Finsler geometry, a more advanced mathematical language," says Heefer.

Field equations

To explore the possibilities of Finsler gravity, Heefer needed to analyze and solve a certain field equation.

Physicists like to describe everything in nature in terms of fields. In physics, a field is simply something that has a value at each point in space and time.

A simple example would be temperature, for instance; at any given point in time, each point in space has a certain temperature associated with it.

A slightly more complex example is that of the electromagnetic field. At any given point in time, the value of the electromagnetic field at a certain point in space tells us the direction and magnitude of the electromagnetic force that a charged particle, like an electron, would experience if it were located at that point.

When it comes to the geometry of spacetime itself, that is also described by a field, namely the gravitational field. The value of this field at a point in spacetime tells us the curvature of spacetime at that point, and it is this curvature that manifests itself as gravity.

Heefer turned to the Christian Pfeifer and Mattias N. R. Wohlfarth's vacuum field equation, which is the equation that governs this gravitational field in empty space. In other words, this equation describes the possible shapes that the geometry of spacetime could take in the absence of matter.

Heefer explains, "To good approximation, this includes all interstellar space between stars and galaxies, as well as the empty space surrounding objects such as the sun and the Earth. By carefully analyzing the field equation, several new types of spacetime geometries have been identified."

Gravitational waves confirmation

One particularly exciting discovery from Heefer's work involves a class of spacetime geometries that represent gravitational waves—ripples in the fabric of spacetime that propagate at the speed of light and can be caused by the collision of neutron stars or black holes, for example.

The first direct detection of gravitational waves on September 14, 2015, marked the dawn of a new era in astronomy, allowing scientists to explore the universe in an entirely new way.

Since then, many observations of gravitational waves have been made. Heefer's research indicates that these are all consistent with the hypothesis that our spacetime has a Finslerian nature.

Scratching the surface

While Heefer's results are promising, they only scratch the surface of the implications of the field equation of Finsler gravity.

"The field is still young and further research in this direction is actively ongoing," says Heefer. "I'm optimistic that our results will prove instrumental in deepening our understanding of gravity and I hope that, eventually, they may even shine light on the reconciliation of gravity with quantum mechanics."

More information:S.J. Heefer, Finsler Geometry, Spacetime & Gravity (2024)

Provided byEindhoven University of Technology

Citation:Gravitational waves and the geometry of spacetime (2024, June 4)retrieved 13 June 2024from

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Gravitational waves and the geometry of spacetime (2024)


How do gravitational waves affect spacetime? ›

A perfectly symmetrical collapse of a supernova will produce no waves, but a non-spherical one will emit gravitational radiation. A binary system will always radiate. Gravitational waves distort spacetime: they change the distances between large, free objects.

Is gravity the geometry of spacetime? ›

And when it comes to the geometry of spacetime itself, that is also described by a field, namely the gravitational field. The value of this field at a point in spacetime tells us the curvature of spacetime at that point, and it is this curvature that manifests itself as gravity.

What did Einstein say about gravitational waves? ›

Albert Einstein's general theory of relativity predicted the existence of gravitational waves — distortions in spacetime — but assumed that they would be virtually impossible to detect from Earth.

What is the theory that says that gravity is a result of the geometry of space? ›

General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics.

How does gravity distort spacetime? ›

When light passes close to a massive object, space-time is so warped that it curves the path the light must follow. Light that would normally go through the galaxy cluster bends around it, producing intensified – and sometimes multiple – images of the source.

Can gravity manipulate time and space? ›

We know that the presence of mass and energy warp spacetime - and the most intense part of that warping is in time - our gravitational time dilation. Things closer to the Earth move through time more slowly. We can show this as a bunch of identical clocks. They tick as they move up.

Can spacetime exist without gravity? ›

General relativity tells us that what we call space is just another feature of the gravitational field of the universe, so space and space-time can and do not exist apart from the matter and energy that creates the gravitational field.

What is the spacetime theory of gravity? ›

Gravity as Curved Spacetime

Gravity feels strongest where spacetime is most curved, and it vanishes where spacetime is flat. This is the core of Einstein's theory of general relativity, which is often summed up in words as follows: "matter tells spacetime how to curve, and curved spacetime tells matter how to move".

What is spacetime geometry? ›

In physics, spacetime is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects such as how different observers perceive where and when events occur.

Is gravity a wave or a force? ›

Gravity isn't just a force that keeps things glued together. Through our understanding of general relativity, we know that gravity can make gravitational waves, or ripples in the fabric of space-time.

What causes the most powerful gravitational waves? ›

The strongest gravitational waves are produced by cataclysmic events such as colliding black holes, supernovae (massive stars exploding at the end of their lifetimes), and colliding neutron stars.

Do gravitational waves affect us? ›

Gravitational waves are constantly passing Earth; however, even the strongest have a minuscule effect and their sources are generally at a great distance.

What is the paradox of gravity? ›

Kipper A gravitational paradox occurs when the laws of gravity are extended to an infinite universe. The law of gravitation is expressed by differential equations for the metric tensor g~, of the general theory of relativity or by a differential equation for the potential U in a nonrelativistic approximation.

Is gravity a theory or a theorem? ›

A Theory explains the mechanisms behind the phenomena. That is, it describes why it happens. Because the theory of gravity is not a theory about the existence of gravity. The theory takes the existence of gravity as a given, and from there answers questions about why it exists and how it works.

What is the logic behind gravity? ›

However, for most applications, gravity is well approximated by Newton's law of universal gravitation, which describes gravity as a force causing any two bodies to be attracted toward each other, with magnitude proportional to the product of their masses and inversely proportional to the square of the distance between ...

How is space affected by gravity? ›

Every object in space exerts a gravitational pull on every other, and so gravity influences the paths taken by everything traveling through space. It is the glue that holds together entire galaxies. It keeps planets in orbit. It makes it possible to use human-made satellites and to go to and return from the Moon.

What is the gravitational wave memory effect? ›

Gravitational memory effects, also known as gravitational-wave memory effects are predicted persistent changes in the relative position of pairs of masses in space due to the passing of a gravitational wave. Detection of gravitational memory effects has been suggested as a way of validating general relativity.

Does gravity compress space-time? ›

This makes it possible to associate the expansion of space-time with gravity. The effect is manifested immensely increased in the surface of the stellar objects, and then the surface pushes to the surrounding space-time. This accelerated broadening is gravity.

How does a gravitational field effect time? ›

The gravitational field is really a curving of space and time. The stronger the gravity, the more spacetime curves, and the slower time itself proceeds. We should note here, however, that an observer in the strong gravity experiences his time as running normal.


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